PRL 94, 097002 (2005)
PHYSICAL REVIEW LETTERS
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Superconductivity in the Americium Metal as a Function of Pressure:
Probing the Mott Transition
J.-C. Griveau, J. Rebizant, and G. H. Lander
European Commission, Joint Research Centre, Institute for Transuranium, Elements Postfach 2340, 76125 Karlsruhe, Germany
G. Kotliar
Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
(Received 29 January 2004; published 7 March 2005)
High-pressure measurements of the resistivity of americium metal are reported to 27 GPa and down to
temperatures of 0.4 K. The unusual dependence of the superconducting temperature (Tc ) on pressure is
deduced. The critical field [Hc 0 extrapolated to T 0] increases dramatically from 0.05 to 1 T as the
pressure is increased, suggesting that the type of superconductivity is changing as pressure increases. At
pressures of 16 GPa the 5f electrons of Am are changing from localized to itinerant, and the crystal
structure also transforms to a complex one. The role of a Mott-type transition in the development of the
peak in Tc above 16 GPa is postulated.
DOI: 10.1103/PhysRevLett.94.097002
PACS numbers: 74.25.Fy, 74.25.Op, 74.62.Fj
Americium is the first actinide element in which, at
ambient pressures, the 5f electrons may be described as
localized (as is found, for example, in most of the 4f rareearth series) and thus do not participate in the bonding.
Am3 has an electronic ground state with a J 0 singlet,
so that (in Russell-Saunders coupling) L S 3 and no
magnetic moment exists. A similar conclusion is reached
starting from the jj coupling scheme, Am3 with six f
electrons has a full j 5=2 shell. This simple picture of
Am metal, whereby six f electrons form an inert core,
decoupled from the spd electrons that control the physical
properties of the material, led to the prediction [1] in 1975
of superconductivity in Am, a prediction soon verified [2]
showing Tc 0:79 K. A decade ago equipment became
available in the Institute of Transuranium Elements in
Karlsruhe to measure the resistivity of active materials
under pressure, and early work [3] showed that Tc rapidly
increased with pressures in the GPa range. At that time the
minimum temperature of the equipment was 1:3 K, and
no magnetic field was available to estimate Hc .
The interest in Am under pressure increased with the
elegant experiments determining the crystal structures
[4,5] as a function of pressure up to 100 GPa. In this pressure range, Am exhibits three phase transitions. The first
between Am I (dhcp crystal structure) and Am II (fcc
structure) involves only a small reduction in volume. The
second phase transition occurs at 11 GPa with the development of Am III—an orthorhombic Fddd structure,
which is also found in the -Pu phase at high temperature.
This transition involves a small contraction of 2% in the
volume of the unit cell. At 16 GPa a third phase transition
occurs into the Am IV phase (Pnma structure, close to that
of -uranium) with a 7% relative volume collapse.
As proposed in Ref. [1], at ambient pressure Am I can
be described as a localized system in which the 5f electrons do not participate in the bonding. On the other hand,
0031-9007=05=94(9)=097002(4)$23.00
in Am IV the bulk modulus is substantially larger
(100 GPa) than in the other three preceding phases
(30 GPa), suggesting that the 5f electrons in this phase
are fully delocalized and participate in the bonding [5].
Indeed, density functional calculations with the 5f electrons treated as core states give an equilibrium volume [6]
close to that of Am I and obtained Am IV as the stable
phase at high pressures [7]. These studies predict an abrupt
Mott transition with a large volume collapse of the order of
25% to 30% on passing to Am IV.
The experiments of Refs. [4,5] raise the fundamental
question of how the Mott transition (i.e., the evolution of
the f electrons from the localized to the itinerant limit)
takes place in Am metal. Am offers a perspective on the
Mott phenomena complementary to the one obtained from
Pu, its immediate neighbor in the periodic table. First, in all
the phases of Pu, the f electrons are itinerant (even though
in -Pu the f states are at the brink of localization [8,9]),
whereas in Am the actual transition between a localized to
an itinerant f electron is realized. Second, Pu has an open
shell of f electrons, whereas Am, at least in the initial state,
is closer to a full j 5=2 shell.
In this Letter we experimentally address these issues and
their impact on the superconductivity of Am. Measurements have been performed at the Institute for Transuranium Elements, Karlsruhe, on thin foils of americium
metal (243 Am; t1=2 7:38 103 yr) with the dhcp structure. Two samples (A and B) were extracted from the same
batch as in Ref. [3]. The dimensions of samples A and B
were, respectively, 600 70 30 m3 and 550 80 30 m3 . The low amount of material (<100 g) reduced
the self-heating effect (6:3 mW=g) due to alpha decay. The
resistance of the sample was measured by a four probe dc
technique with the sample and a thin foil of lead (manometer) held in a pyrophyllite gasket and with a solid
pressure-transmitting medium of steatite. The external
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 2005 The American Physical Society
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PHYSICAL REVIEW LETTERS
PRL 94, 097002 (2005)
pressure device was a piston-cylinder system made of
nonmagnetic CuBe, with the pressure generated by two
1.5 mm diameter anvils made of low-magnetic tungsten
carbide and sintered diamonds [3]. We adapted a 3 He refrigerator to cool the pressure device to temperatures of
275 mK. Self-heating effects prevented cooling of the
sample below 400 mK. An external superconducting
magnet allowed a maximum magnetic field of 0.6 T to be
applied.
Figure 1 displays the resistance as a function of T; p
for 243 Am up to pmax 27 GPa and down to Tmin 0:4 K. Overall, the measurements reproduce well the behavior previously reported, but they are now extended to
below 0.8 K, the ambient pressure Tc , and a small magnetic
field can be applied (see below). We note that the residual
resistivity ratio (RRR) of the present sample as presented
in Fig. 1 is considerably better than those shown in Ref. [3].
Am III - Am IV
600
400
Am I - Am II
200
ρ (µΩ.cm)
Am II - Am III
0
30
300
200
This better RRR, probably due to having a better grain
structure in our sample, allows more quantitative deduction
of the superconducting parameters.
The strong increase of resistivity as a function of increasing pressure [3,10] and temperature [3,11] have been
noted before and appear as an intrinsic property of Am that
is not observed in other (lighter) actinides. These observations suggest that the f electrons play an important role in
the transport properties, strongly scattering the spd conduction electrons when they are localized, and contributing
to the transport when they are itinerant.
Figure 2 shows Tc as a function of fractional volume
shift V=V0 , where V V0 Vp, with V0 the atomic
volume at ambient pressure. The figure exhibits a rich
behavior with two maxima, one near the Am I–Am II
boundary and the second very sharp maximum within the
Am IV phase. At the highest pressures, Tc decreases with
pressure with a slope of 0:15 K=GPa (Fig. 2) and is
extrapolated to disappear at around 55% of the initial
volume (30 GPa). Both Am II and Am III remain superconductors at all temperatures, a point that was not established in the previous work. The inset shows measurements
to determine critical field Hc T at V=V0 0:39, corresponding to 20.8 GPa. The width of the superconducting
transition temperature (Tc 100 mK) indicates good
hydrostatic pressure conditions.
The first important result of our studies is the very sharp
maximum in Tc as observed in Am IV just as the compressibility data [4,5] show that the bulk modulus has
changed, a complicated -uranium-like structure is
adopted, and, according to all calculations, the 5f electrons
20
T ( 100
K)
0
a)
GP
p(
10
0
2.5
Am III
Am II
Am I
Sample A
Sample B
2.0
50
25
ρ (µΩ.cm)
75
Am I - Am II
1.5
T (K
)
0.5
10
0.0 0
B=0.6T
40
B=0.0T
0
0.0
0.5
0.0
0.5
1.0
1.5
2.0
T (K)
0.1
0.2
0.3
0.4
0.5
∆V/V0
20
1.0
p=20.8 GPa
60
20
30
2.0
80
1.0
0
2.5
1.5
ρ (µΩ .cm )
Tc(K)
100
Am III - Am IV
Am II - Am III
3.0
Am IV
Pa)
p (G
FIG. 1 (color). Overview of the resistivity data as a function of
pressure and temperature. The phase boundaries (taken from
Refs. [4,5]) are shown. The lower figure shows the same data but
only up to a maximum of 3 K, to show clearly the superconducting region.
FIG. 2. The superconducting temperature Tc plotted as a function of fractional volume shift V=V0 , where V V0 Vp,
with V0 the atomic volume at ambient pressure. Tc is determined
as the midheight of the transition. The inset shows the change of
resistivity as a function of applied magnetic field at an atomic
volume corresponding to the maximum within the Am IV phase.
The shaded areas represent the transition between the different
phases.
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This point may be addressed by calculating the meanfree path l and the coherence length 0 from resistivity and
critical field measurements and determining if the material
changes from a clean metal superconductor (in the ‘‘clean
limit,’’ l 0 ) to a ‘‘dirty superconductor’’ (l 0 ).
Considering the relation between l and [17], we assume
Am has three delocalized spd electrons for all pressures in
this region. For 0 , we assume either type-I or type-II
superconductivity. Type-I superconductivity implies relations between Tc p, the unit cell volume under pressure,
and Hc 0 [18] only. For type II, Hc 0 is assimilated into
Hc2 , and we extract the intermediate parameter GL [19].
0 is finally determined according to the ‘‘clean’’ or ‘‘dirty
limit’’ scenario with lp considered in addition [18,19]. l,
GL , and 0 estimated according to the type-II dirty limit
scenario are presented in Fig. 4. We can also deduce the
Sommerfeld coefficient [18,19].
At the highest pressures (where the superconductivity is
of type II in the dirty limit) the value is derived to be
modest ( 60 mJ mol1 K2 ). Am IV at these high pressures (>20 GPa) is a metal with itinerant 5f and spd electrons spread out over a large energy near EF , so this modest
Hc (T)
1.5
1.25
Am I Am II Am III
Am IV
1.00
Am III
Am IV
Type I
Type II
Smith et al
Mueller et al
100
Cross over
Type I-Type II
1.50
Hc(0) (T)
0.0 GPa
1.9 GPa
2.2 GPa
4.3 GPa
5.5 GPa
2
Hc(0)(1-(T/Tc) )
Am II
Am I
-1
-2
γ (mJ.mol .K )
1000
10
1000
100
0.75
ξ0
ξGL
0.50
1.0
0
0.00
0
10
20
30
0.0
1
2
3
5
10
15
20
25
P (GPa)
P (GPa)
0
10
1
0.25
0.5
length (nm)
have become itinerant; i.e., the Mott transition has occurred. The maximum of Tc in the proximity to the Mott
transition can be understood on very general grounds. At
very large pressures, the transition temperature decreases
since the f kinetic energy becomes large compared to the
pairing interactions (i.e., the f density of states is reduced).
At smaller pressures in the Am III phase, the decrease in
pressure localizes the f electrons, which therefore cannot
superconduct. These ideas have recently been supported by
explicit dynamical mean field calculations [12]. Here these
ideas are realized in an element. With decreasing pressure,
the dramatic decrease in the bulk modulus when progressing from the Am IV to Am III phase is an experimental
proof of the localization of the 5f electrons upon entering
Am III.
Previous studies at ambient pressure [13] indicate Am
is a type-I superconductor with a relatively high zerotemperature critical field Hc 0 53 mT compared to
other BCS superconducting elements [14] considering its
low Tc [15]. The pressure dependence of the upper critical
fields measured here is surprising, with Hc 0 increasing
rapidly with pressure as shown in Fig. 3 and attaining a
value of over 1 T at the maximum of Tc . This feature has
already been observed in some elements at structural phase
transitions (Ga), and a change of type of superconductivity
is observed [16]. Since a critical field of 1 T would be most
unusual for a type-I superconductor with Tc 2:3 K, the
following question must be raised: Does Am become a
type-II superconductor under pressure?
2.0
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PHYSICAL REVIEW LETTERS
PRL 94, 097002 (2005)
4
Tc (K)
FIG. 3. The critical field Hc T for various pressures with the
extrapolations to Hc 0. The inset shows the extrapolated critical
field to T 0, Hc 0, as a function of pressure. Note that the
Hc 0 has been deduced with the empirical Hc 0 1 t2 law
with t T=Tc p. The dependence of this extrapolation will
change depending on the type of superconductivity assumed.
Assuming Am as the type II superconductor and using the
Werthamer-Helfand-Hohenberg approximation [22] to determine the orbital critical field Hc2 0 leads to similar values.
Therefore, the exact value of Hc 0 [or Hc2 0] is not crucial;
whatever form is used Hc 0 [or Hc2 0] increases dramatically
as a function of pressure.
FIG. 4 (color). Upper curves: (Sommerfeld) coefficients deduced from the superconducting properties. Open triangles
(circles) assuming type-I (type-II) superconductivity. The solid
diamond is derived in Ref. [13] from the superconducting properties. The solid square is the value obtained in Ref. [13,20] by
direct specific-heat measurements. The lower curves show the
mean-free path (l) (open triangles) and the coherence lengths
(0 , GL ) as deduced assuming (1) BCS (solid squares) in the
clean limit and (2) Ginzburg-Landau in the dirty limit (solid
circles). The drastic decrease of l with pressure (2 orders of
magnitude) is directly related to the huge increase of resistivity
at low temperature (l 1= in the free electron approximation
[17]). This implies an important scattering process that leads to
an increase of magnetic penetration depth ("L ) and a decrease of
superconducting coherence length (0 ), and therefore to a possible change in the type of superconductivity [18].
097002-3
PRL 94, 097002 (2005)
PHYSICAL REVIEW LETTERS
specific heat is credible. At the Am III phase (p < 16 GPa)
the 5f states move through EF on their way to localization.
The coefficient therefore increases when approaching the
Am III–Am IV boundary. As the pressure is further reduced into Am II and then Am I, the Sommerfeld coefficient appears to increase further; however, this is not a
reasonable result, indicating that the hypothesis of type II
superconductivity is no longer correct. At the lowest pressures the form of the superconductivity becomes difficult
to characterize, a point already emphasized by Smith et al.
in their earlier work on this system [13]. The open triangles
show our deduction of assuming type-I superconductivity. This is in good agreement with the value of
200 mJ mol1 K2 (solid diamonds) given in Ref. [13] as
deduced also from the superconducting properties. On the
other hand, these values are in sharp disagreement with the
value of 3 mJ mol1 K2 deduced from specific-heat
experiments [13,20] (solid squares). At low pressure the
mean-free path becomes shorter than the coherence length
(inset of Fig. 4), which is another indication that there is a
change from type I (or some complicated) superconductivity at low pressures to type II at higher pressures. The
precise physics of the superconductivity in the lowpressure range remains poorly defined.
A major challenge is to understand a broad maximum
(Fig. 2) in Tc as a function of pressure in the range of
pressures corresponding to Am I and Am II, when the
5f states are still localized. At zero pressure, Am metal
is well described by an inert atomic occupied 5f6 configuration at each lattice site and an itinerant spd band containing three electrons. As pressure is applied, the energy
of another configuration approaches the Fermi level, and
begins to be admixed into the ground state, a fact that can
account for the increase in room temperature resistivity,
and the maximum of Tc , which in a mixed valence fluctuation mechanism occurs when the configurations 5f6 and
5f5 sd1 (or 5f6 sd1 and 5f7 at the Fermi level) become
degenerate. These ideas were proposed in connection with
CeCu2 Si2 [21].
Across this total pressure range (up to 27 GPa) there
is no sign of any transition to ordered magnetism, as
judged by an anomaly in the resistivity, in contrast to the
predictions of Söderlind et al. [6]. It would be interesting to perform specific-heat experiments of Am at low
temperature and with modest pressures, as the exact form
of the superconductivity at low pressures is not well
established.
With elements such as americium the difficulty of manipulating the material has discouraged much experimental
work. On the other hand, the extreme simplicity of the halffilled j 5=2 shell of localized 5f electrons in ambientpressure americium and the change as a function of pres-
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sure would appear to be a textbook example of the Mott
transition. Indeed, theory has predicted a volume collapse
of between 25% and 30% [6,7]. This is clearly far too
simple. The structural study [4,5] shows that the volume
changes are small, at most 7% between Am III and Am IV.
Despite this, there is a very sharp increase in Tc as a
function of pressure (see Fig. 2) that we attribute directly
to the Mott transition when the 5f states pass through the
Fermi level.
J. C. G. acknowledges the members of the workshop at
ITU for valuable contributions over a number of years. We
thank Joe Thompson, Jason Lashley, James Smith (Los
Alamos), and Ladia Havela (Charles University, Prague)
for useful discussions. This work was supported by
‘‘Training and Mobility of Researchers’’ program of
European Union (Project No. EU 2000/30/02). The Am
metal for these experiments was provided by Dr. R. Haire
of Oak Ridge National Laboratory, and we especially thank
him for this supply and purification at ORNL. G. K. is
supported by DOE-DE-FG02-99ER45761.
[1] B. Johansson and A. Rosengren, Phys. Rev. B 11, 2836
(1975).
[2] J. L. Smith and R. G. Haire, Science 200, 535 (1978).
[3] P. Link et al., J. Alloys Compd. 213–214, 148 (1994).
[4] S. Heathman et al., Phys. Rev. Lett. 85, 2961 (2000).
[5] A. Lindbaum et al., Phys. Rev. B 63, 214101 (2001).
[6] P. Söderlind et al., Phys. Rev. B 61, 8119 (2000).
[7] M. Penicaud, J. Phys. Condens. Matter 14, 3575 (2002).
[8] B. Johansson, Phys. Rev. B 11, 2740 (1975).
[9] S. Savrasov, G. Kotliar, and E. Abrahams, Nature
(London) 410, 793 (2001).
[10] D. R. Stephens et al., J. Phys. Chem. Solids 29, 815
(1968).
[11] R. Schenkel and W. Mueller, J. Phys. Chem. Solids 38,
1301 (1977).
[12] M. Capone et al., Science 296, 2364 (2002).
[13] J. L. Smith et al., J. Phys. (Paris) 40, C4-138 (1979).
[14] A. C. Rose-Innes and E. H. Rhoderick, Introduction to
Superconductivity (Pergamon Press, New York, 1978),
2nd ed., p. 7.
[15] J. Bardeen et al., Phys. Rev. 108, 1175 (1957).
[16] J. Feder et al., Solid State Commun. 4, 611 (1966).
[17] N. W. Ashcroft and N. D. Mermin, Solid State Physics
(Saunders College Publishing, Cornell University, Ithaca,
NY, 1976).
[18] M. Tinkham, Introduction to Superconductivity (McGrawHill, New York, 1975).
[19] T. P. Orlando et al., Phys. Rev. B 19, 4545 (1979).
[20] W. Mueller et al., J. Low Temp. Phys. 30, 561 (1978).
[21] A. Holmes et al., Phys. Rev. B 69, 024508 (2004).
[22] N. R. Werthamer et al., Phys. Rev. 147, 295 (1966).
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